Comments on fusion matrix in N=1 super Liouville field theory

We study several aspects of the $N=1$ super Liouville theory. We show that certain elements of the fusion matrix in the Neveu-Schwarz sector related to the structure constants according to the same rules which we observe in rational conformal field theory. We collect some evidences that these relations should hold also in the Ramond sector. Using them the Cardy-Lewellen equation for defects is studied, and defects are constructed.Comment: 28 pages, comment and reference adde

Defects, Non-abelian T-duality, and the Fourier-Mukai transform of the Ramond-Ramond fields

We construct topological defects generating non-abelian T-duality for isometry groups acting without isotropy. We find that these defects are given by line bundles on the correspondence space with curvature which can be considered as a non-abelian generalization of the curvature of the Poincar\`{e} bundle. We show that the defect equations of motion encode the non-abelian T-duality transformation. The Fourier-Mukai transform of the Ramond-Ramond fields generated by the gauge invariant flux of these defects is studied. We show that it provides elegant and compact way of computation of the transformation of the Ramond-Ramond fields under the non-abelian T-duality.Comment: 18 pages, minor typos corrected, references adde

On mini-superspace limit of boundary three-point function in Liouville field theory

We study mini-superspace semiclassical limit of the boundary three-point function in the Liouville field theory. We compute also matrix elements for the Morse potential quantum mechanics. An exact agreement between the former and the latter is found. We show that both of them are given by the generalized hypergeometric functions.Comment: 18 page

On classical and semiclassical properties of the Liouville theory with defects

The Lagrangian of the Liouville theory with topological defects is analyzed in detail and general solution of the corresponding defect equations of motion is found. We study the heavy and light semiclassical limits of the defect two-point function found before via the bootstrap program. We show that the heavy asymptotic limit is given by the exponential of the Liouville action with defects, evaluated on the solutions with two singular points. We demonstrate that the light asymptotic limit is given by the finite dimensional path integral over solutions of the defect equations of motion with a vanishing energy-momentum tensor.Comment: 50 pages, typos corrected, references added, comments and explanations adde

Photon-number selective group delay in cavity induced transparency

We show that the group velocity of a probe pulse in an ensemble of $\Lambda$-type atoms driven by a quantized cavity mode depends on the quantum state of the input probe pulse. In the strong-coupling regime of the atom-cavity system the probe group delay is photon number selective. This can be used to spatially separate the single photon from higher photon-number components of a few-photon probe pulse and thus to create a deterministic single-photon source.Comment: 5 pages, 2 figures. revised versio

Topological defects in the Liouville field theories with different cosmological constants

We construct topological defects in the Liouville field theory producing jump in the value of cosmological constant. We construct them using the Cardy-Lewellen equation for the two-point function with defect. We show that there are continuous and discrete families of such kind of defects. For the continuous family of defects we also find the Lagrangian description and check its agreement with the solution of the Cardy-Lewellen equation using the heavy asymptotic semiclasscial limit.Comment: 15 page

From rarefied elliptic beta integral to parafermionic star-triangle relation

We consider the rarefied elliptic beta integral in various limiting forms. In particular, we obtain an integral identity for parafermionic hyperbolic gamma functions which describes the star-triangle relation for parafermionic Liouville theory.Comment: 19 page